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Solids:

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Clearly, an anvil is a solid

A solid is a state of matter in which the intermolecular forces, or forces between molecules, are strong enough to hold the molecules in a fixed position except for slight vibrational motion. This causes solids to have a fixed volume and shape. The molecules of a solid are tightly packed together with little space between them, and therefore are practically incompressible. There are four types of solids: Molecular, Ionic, Covalent, and Network Covalent. Molecular solids are held together by intermolecular forces, such as sugar. Covalent solids are solids that form a large, continuous chain of covalently bonded molecules, such as diamonds. Ionic solids consist of ions with opposing forces held together by electrostatic attraction. Ionic solids are generally highly crystalline, a concept which will be explained later. Metallic solids consist of a positively charged region of metallic nuclei surrounded by a contiunally dissociating region of negatively charged electrons. The latter three types of solids are considered network solids. In a network solid, there are no distinct molecules or clusters within the atom rather the array of molecules extends uniformly throughout the solid. Network solids can form multidimensional networks. In a single dimensional network, the solid will become waxy, or plastic-like solids. In a two-dimensional network, the solid has multiple planes of atoms that can slide over each other. Two-dimensional solids can easily form lubricants. A three dimensional solid generally forms a very hard, generally metallic substance. The proximity of molecules of a solid as compared to other states of matter impacts its density. Typically (for the exception and explanation see here) as a substance cools its molecules compress together, therefore decreasing the volume of any given amount of particles will occupy. If - for a given number of particles (implying a given mass) - the volume occupied is decreased, the density inherently increases. The molecules of a solid order themselves in a regular pattern. Solids that are highly ordered are considered to be crystalline. The difference in structures between a crystalline solid and an amorphous solid (the most irregular form of solid) is seen below.
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A comparison of crystalline and non-crystalline solids

Liquids:

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Pepto Bismol is a fun, pink, liquid.

What causes Pepto Bismol to have that smooth slide down your throat? Again, it is intermolecular forces. The intermolecular forces present in a liquid are strong enough to hold the molecules close together. However, these forces are not strong enough to hold the molecules in a rigid position so the molecules of a liquid are free to move relative to each other. That causes the liquid to assume the shape of its container, or be poured from one container to another. Based on these intermolecular forces, liquids have a fixed volume, but assume the shape of their container. Interesting characteristics of liquids are caused by their intermolecular forces. Liquids, like gases, seek to expand to fill their container, but because their intermolecular forces resist the increase of surface area, and create surface tension. Because the molecules of a liquid are relatively close to one another, liquids are almost incompressible. The density of a liquid is between that of a gas and a solid because the molecules are spread farther apart in a liquid than in a solid, but they are not spread as far apart as those of a gas.

Changing Between States of Matter:

Several factors will cause a substances to change its state of matter. They are:
  • Temperature
  • Pressure
  • Intermolecular Attractive Forces
If a substance's temperature is increased, its kinetic energy is increased and the intermolecular forces are overcome by the fact that molecules are spread far enough apart that their effect lessens. The converse also holds true. If the pressure of a substance is increased, the molecules are forced closer together, and due to intermolecular forces, try to cohere and therefore form liquids/solids more readily. Intermolecular attractive forces impact how readily molecules respond to changes in temperature and pressure. If a substance has high intermolecular attraction, slight changes in temperature/pressure will change the state of matter, whereas a substance such as helium will require severe changes in temperature or pressure in order for its state of matter to change.

Factual Source:
Brown, LeMay, and Bursten: Chemistry, the Central Science.

Picture sources (in order of appearence):
http://www.r-row.com/images/roadrunner2.jpg
http://www.ohsu.edu/research/sbh/resultsimages/crystalvsglass.gif
http://www.firstaidmonster.com/images/products/FAM_PEPTO_BISMOL_LIQ_CHERRY_-5702.jpg